Recently, we have observed a steady increase in interest in mathematical morphology amongst the deep learning community. Indeed, the intrinsic features of mathematical morphology operators that enable them to extract information from topological structures make them excellent candidates.
Morphological operators have been shown to capture image edges [1]}, granulometry [2]}, [3]} and distances to object borders [4]}.
Two methodologies are employed in the literature to evaluate the utility of morphological operators. Some analyses  [5]}, [6]}, [7]} directly extract descriptors from unlearned morphological layers, while others  [8]}, [9]}, [10]} propose learning the structural element of the morphological operators. Despite their superior performance in various application situations, these methodologies are prone to failure if the deep network architecture is misdesigned, which may dissuade researchers from pursuing this research path.
